LMFDB - Embedded newform 1183.2.a.r.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.961590$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.961590 q^{2} -1.98737 q^{3} -1.07534 q^{4} +3.39320 q^{5} +1.91103 q^{6} +1.00000 q^{7} +2.95722 q^{8} +0.949635 q^{9} +O(q^{10})$	\(q-0.961590 q^{2} -1.98737 q^{3} -1.07534 q^{4} +3.39320 q^{5} +1.91103 q^{6} +1.00000 q^{7} +2.95722 q^{8} +0.949635 q^{9} -3.26287 q^{10} +4.59237 q^{11} +2.13711 q^{12} -0.961590 q^{14} -6.74354 q^{15} -0.692948 q^{16} +2.44749 q^{17} -0.913160 q^{18} +4.77408 q^{19} -3.64886 q^{20} -1.98737 q^{21} -4.41598 q^{22} -4.04446 q^{23} -5.87709 q^{24} +6.51382 q^{25} +4.07483 q^{27} -1.07534 q^{28} -3.20889 q^{29} +6.48453 q^{30} -4.83171 q^{31} -5.24811 q^{32} -9.12674 q^{33} -2.35349 q^{34} +3.39320 q^{35} -1.02118 q^{36} +9.61127 q^{37} -4.59071 q^{38} +10.0344 q^{40} -8.99377 q^{41} +1.91103 q^{42} -8.90960 q^{43} -4.93838 q^{44} +3.22230 q^{45} +3.88911 q^{46} -5.37660 q^{47} +1.37714 q^{48} +1.00000 q^{49} -6.26362 q^{50} -4.86407 q^{51} +9.97733 q^{53} -3.91832 q^{54} +15.5829 q^{55} +2.95722 q^{56} -9.48786 q^{57} +3.08564 q^{58} +10.5145 q^{59} +7.25163 q^{60} +5.29731 q^{61} +4.64612 q^{62} +0.949635 q^{63} +6.43243 q^{64} +8.77619 q^{66} +14.0270 q^{67} -2.63190 q^{68} +8.03783 q^{69} -3.26287 q^{70} -8.52794 q^{71} +2.80828 q^{72} +6.62822 q^{73} -9.24211 q^{74} -12.9454 q^{75} -5.13378 q^{76} +4.59237 q^{77} -7.98042 q^{79} -2.35131 q^{80} -10.9471 q^{81} +8.64833 q^{82} -7.30165 q^{83} +2.13711 q^{84} +8.30484 q^{85} +8.56739 q^{86} +6.37725 q^{87} +13.5807 q^{88} +18.1007 q^{89} -3.09854 q^{90} +4.34918 q^{92} +9.60239 q^{93} +5.17009 q^{94} +16.1994 q^{95} +10.4299 q^{96} +6.90825 q^{97} -0.961590 q^{98} +4.36108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.961590	−0.679947	−0.339974	−	0.940435i	$-0.610418\pi$
$2$	−0.961590	−0.679947	−0.339974	+	0.940435i	$0.610418\pi$
$3$	−1.98737	−1.14741	−0.573704	−	0.819063i	$-0.694494\pi$
$3$	−1.98737	−1.14741	−0.573704	+	0.819063i	$0.694494\pi$
$4$	−1.07534	−0.537672
$5$	3.39320	1.51749	0.758743	−	0.651390i	$-0.225814\pi$
$5$	3.39320	1.51749	0.758743	+	0.651390i	$0.225814\pi$
$6$	1.91103	0.780177
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.95722	1.04554
$9$	0.949635	0.316545
$10$	−3.26287	−1.03181
$11$	4.59237	1.38465	0.692326	−	0.721584i	$-0.256586\pi$
$11$	4.59237	1.38465	0.692326	+	0.721584i	$0.256586\pi$
$12$	2.13711	0.616929
$13$	0	0
$13$	0	0
$14$	−0.961590	−0.256996
$15$	−6.74354	−1.74118
$16$	−0.692948	−0.173237
$17$	2.44749	0.593604	0.296802	−	0.954939i	$-0.404080\pi$
$17$	2.44749	0.593604	0.296802	+	0.954939i	$0.404080\pi$
$18$	−0.913160	−0.215234
$19$	4.77408	1.09525	0.547625	−	0.836724i	$-0.315532\pi$
$19$	4.77408	1.09525	0.547625	+	0.836724i	$0.315532\pi$
$20$	−3.64886	−0.815910
$21$	−1.98737	−0.433679
$22$	−4.41598	−0.941491
$23$	−4.04446	−0.843328	−0.421664	−	0.906752i	$-0.638554\pi$
$23$	−4.04446	−0.843328	−0.421664	+	0.906752i	$0.638554\pi$
$24$	−5.87709	−1.19966
$25$	6.51382	1.30276
$26$	0	0
$27$	4.07483	0.784202
$28$	−1.07534	−0.203221
$29$	−3.20889	−0.595876	−0.297938	−	0.954585i	$-0.596299\pi$
$29$	−3.20889	−0.595876	−0.297938	+	0.954585i	$0.596299\pi$
$30$	6.48453	1.18391
$31$	−4.83171	−0.867800	−0.433900	−	0.900961i	$-0.642863\pi$
$31$	−4.83171	−0.867800	−0.433900	+	0.900961i	$0.642863\pi$
$32$	−5.24811	−0.927744
$33$	−9.12674	−1.58876
$34$	−2.35349	−0.403620
$35$	3.39320	0.573556
$36$	−1.02118	−0.170197
$37$	9.61127	1.58008	0.790042	−	0.613053i	$-0.210059\pi$
$37$	9.61127	1.58008	0.790042	+	0.613053i	$0.210059\pi$
$38$	−4.59071	−0.744712
$39$	0	0
$40$	10.0344	1.58659
$41$	−8.99377	−1.40459	−0.702296	−	0.711885i	$-0.747842\pi$
$41$	−8.99377	−1.40459	−0.702296	+	0.711885i	$0.747842\pi$
$42$	1.91103	0.294879
$43$	−8.90960	−1.35870	−0.679351	−	0.733814i	$-0.737739\pi$
$43$	−8.90960	−1.35870	−0.679351	+	0.733814i	$0.737739\pi$
$44$	−4.93838	−0.744489
$45$	3.22230	0.480353
$46$	3.88911	0.573418
$47$	−5.37660	−0.784258	−0.392129	−	0.919910i	$-0.628261\pi$
$47$	−5.37660	−0.784258	−0.392129	+	0.919910i	$0.628261\pi$
$48$	1.37714	0.198773
$49$	1.00000	0.142857
$50$	−6.26362	−0.885810
$51$	−4.86407	−0.681106
$52$	0	0
$53$	9.97733	1.37049	0.685246	−	0.728312i	$-0.259695\pi$
$53$	9.97733	1.37049	0.685246	+	0.728312i	$0.259695\pi$
$54$	−3.91832	−0.533216
$55$	15.5829	2.10119
$56$	2.95722	0.395175
$57$	−9.48786	−1.25670
$58$	3.08564	0.405165
$59$	10.5145	1.36888	0.684438	−	0.729071i	$-0.260047\pi$
$59$	10.5145	1.36888	0.684438	+	0.729071i	$0.260047\pi$
$60$	7.25163	0.936181
$61$	5.29731	0.678252	0.339126	−	0.940741i	$-0.389869\pi$
$61$	5.29731	0.678252	0.339126	+	0.940741i	$0.389869\pi$
$62$	4.64612	0.590058
$63$	0.949635	0.119643
$64$	6.43243	0.804054
$65$	0	0
$66$	8.77619	1.08027
$67$	14.0270	1.71367	0.856837	−	0.515588i	$-0.172426\pi$
$67$	14.0270	1.71367	0.856837	+	0.515588i	$0.172426\pi$
$68$	−2.63190	−0.319164
$69$	8.03783	0.967641
$70$	−3.26287	−0.389988
$71$	−8.52794	−1.01208	−0.506040	−	0.862510i	$-0.668891\pi$
$71$	−8.52794	−1.01208	−0.506040	+	0.862510i	$0.668891\pi$
$72$	2.80828	0.330959
$73$	6.62822	0.775775	0.387887	−	0.921707i	$-0.373205\pi$
$73$	6.62822	0.775775	0.387887	+	0.921707i	$0.373205\pi$
$74$	−9.24211	−1.07437
$75$	−12.9454	−1.49480
$76$	−5.13378	−0.588885
$77$	4.59237	0.523350
$78$	0	0
$79$	−7.98042	−0.897867	−0.448934	−	0.893565i	$-0.648196\pi$
$79$	−7.98042	−0.897867	−0.448934	+	0.893565i	$0.648196\pi$
$80$	−2.35131	−0.262885
$81$	−10.9471	−1.21634
$82$	8.64833	0.955048
$83$	−7.30165	−0.801460	−0.400730	−	0.916196i	$-0.631244\pi$
$83$	−7.30165	−0.801460	−0.400730	+	0.916196i	$0.631244\pi$
$84$	2.13711	0.233177
$85$	8.30484	0.900786
$86$	8.56739	0.923845
$87$	6.37725	0.683713
$88$	13.5807	1.44770
$89$	18.1007	1.91867	0.959337	−	0.282265i	$-0.0910856\pi$
$89$	18.1007	1.91867	0.959337	+	0.282265i	$0.0910856\pi$
$90$	−3.09854	−0.326614
$91$	0	0
$92$	4.34918	0.453434
$93$	9.60239	0.995721
$94$	5.17009	0.533254
$95$	16.1994	1.66203
$96$	10.4299	1.06450
$97$	6.90825	0.701426	0.350713	−	0.936483i	$-0.385939\pi$
$97$	6.90825	0.701426	0.350713	+	0.936483i	$0.385939\pi$
$98$	−0.961590	−0.0971353
$99$	4.36108	0.438305
$100$	−7.00459	−0.700459
$101$	6.10247	0.607218	0.303609	−	0.952797i	$-0.401808\pi$
$101$	6.10247	0.607218	0.303609	+	0.952797i	$0.401808\pi$
$102$	4.67725	0.463116
$103$	−3.66700	−0.361320	−0.180660	−	0.983546i	$-0.557823\pi$
$103$	−3.66700	−0.361320	−0.180660	+	0.983546i	$0.557823\pi$
$104$	0	0
$105$	−6.74354	−0.658102
$106$	−9.59411	−0.931862
$107$	9.82398	0.949720	0.474860	−	0.880061i	$-0.342499\pi$
$107$	9.82398	0.949720	0.474860	+	0.880061i	$0.342499\pi$
$108$	−4.38184	−0.421643
$109$	1.51609	0.145215	0.0726074	−	0.997361i	$-0.476868\pi$
$109$	1.51609	0.145215	0.0726074	+	0.997361i	$0.476868\pi$
$110$	−14.9843	−1.42870
$111$	−19.1011	−1.81300
$112$	−0.692948	−0.0654774
$113$	10.7558	1.01182	0.505908	−	0.862587i	$-0.331158\pi$
$113$	10.7558	1.01182	0.505908	+	0.862587i	$0.331158\pi$
$114$	9.12344	0.854488
$115$	−13.7237	−1.27974
$116$	3.45066	0.320386
$117$	0	0
$118$	−10.1107	−0.930764
$119$	2.44749	0.224361
$120$	−19.9421	−1.82046
$121$	10.0899	0.917264
$122$	−5.09385	−0.461175
$123$	17.8739	1.61164
$124$	5.19575	0.466592
$125$	5.13668	0.459439
$126$	−0.913160	−0.0813508
$127$	−11.0034	−0.976390	−0.488195	−	0.872735i	$-0.662345\pi$
$127$	−11.0034	−0.976390	−0.488195	+	0.872735i	$0.662345\pi$
$128$	4.31086	0.381030
$129$	17.7067	1.55899
$130$	0	0
$131$	−7.69627	−0.672426	−0.336213	−	0.941786i	$-0.609146\pi$
$131$	−7.69627	−0.672426	−0.336213	+	0.941786i	$0.609146\pi$
$132$	9.81439	0.854233
$133$	4.77408	0.413965
$134$	−13.4883	−1.16521
$135$	13.8267	1.19001
$136$	7.23778	0.620634
$137$	2.91596	0.249128	0.124564	−	0.992212i	$-0.460247\pi$
$137$	2.91596	0.249128	0.124564	+	0.992212i	$0.460247\pi$
$138$	−7.72910	−0.657945
$139$	7.38529	0.626412	0.313206	−	0.949685i	$-0.398597\pi$
$139$	7.38529	0.626412	0.313206	+	0.949685i	$0.398597\pi$
$140$	−3.64886	−0.308385
$141$	10.6853	0.899864
$142$	8.20039	0.688161
$143$	0	0
$144$	−0.658048	−0.0548373
$145$	−10.8884	−0.904234
$146$	−6.37363	−0.527486
$147$	−1.98737	−0.163915
$148$	−10.3354	−0.849567
$149$	−5.62392	−0.460730	−0.230365	−	0.973104i	$-0.573992\pi$
$149$	−5.62392	−0.460730	−0.230365	+	0.973104i	$0.573992\pi$
$150$	12.4481	1.01639
$151$	−8.87295	−0.722071	−0.361035	−	0.932552i	$-0.617577\pi$
$151$	−8.87295	−0.722071	−0.361035	+	0.932552i	$0.617577\pi$
$152$	14.1180	1.14512
$153$	2.32423	0.187903
$154$	−4.41598	−0.355850
$155$	−16.3950	−1.31687
$156$	0	0
$157$	−14.7335	−1.17586	−0.587929	−	0.808913i	$-0.700056\pi$
$157$	−14.7335	−1.17586	−0.587929	+	0.808913i	$0.700056\pi$
$158$	7.67389	0.610502
$159$	−19.8286	−1.57251
$160$	−17.8079	−1.40784
$161$	−4.04446	−0.318748
$162$	10.5266	0.827050
$163$	17.4467	1.36653	0.683265	−	0.730170i	$-0.260559\pi$
$163$	17.4467	1.36653	0.683265	+	0.730170i	$0.260559\pi$
$164$	9.67140	0.755209
$165$	−30.9689	−2.41092
$166$	7.02120	0.544951
$167$	−12.3209	−0.953422	−0.476711	−	0.879060i	$-0.658171\pi$
$167$	−12.3209	−0.953422	−0.476711	+	0.879060i	$0.658171\pi$
$168$	−5.87709	−0.453427
$169$	0	0
$170$	−7.98585	−0.612487
$171$	4.53364	0.346696
$172$	9.58089	0.730536
$173$	0.540871	0.0411217	0.0205608	−	0.999789i	$-0.493455\pi$
$173$	0.540871	0.0411217	0.0205608	+	0.999789i	$0.493455\pi$
$174$	−6.13231	−0.464889
$175$	6.51382	0.492398
$176$	−3.18228	−0.239873
$177$	−20.8963	−1.57066
$178$	−17.4055	−1.30460
$179$	13.6466	1.02000	0.509999	−	0.860175i	$-0.329646\pi$
$179$	13.6466	1.02000	0.509999	+	0.860175i	$0.329646\pi$
$180$	−3.46509	−0.258272
$181$	1.83569	0.136446	0.0682230	−	0.997670i	$-0.478267\pi$
$181$	1.83569	0.136446	0.0682230	+	0.997670i	$0.478267\pi$
$182$	0	0
$183$	−10.5277	−0.778231
$184$	−11.9604	−0.881729
$185$	32.6130	2.39775
$186$	−9.23356	−0.677038
$187$	11.2398	0.821936
$188$	5.78169	0.421673
$189$	4.07483	0.296400
$190$	−15.5772	−1.13009
$191$	−10.1490	−0.734356	−0.367178	−	0.930151i	$-0.619676\pi$
$191$	−10.1490	−0.734356	−0.367178	+	0.930151i	$0.619676\pi$
$192$	−12.7836	−0.922577
$193$	−4.66529	−0.335815	−0.167908	−	0.985803i	$-0.553701\pi$
$193$	−4.66529	−0.335815	−0.167908	+	0.985803i	$0.553701\pi$
$194$	−6.64291	−0.476933
$195$	0	0
$196$	−1.07534	−0.0768103
$197$	9.10037	0.648375	0.324187	−	0.945993i	$-0.394909\pi$
$197$	9.10037	0.648375	0.324187	+	0.945993i	$0.394909\pi$
$198$	−4.19357	−0.298024
$199$	−13.4461	−0.953168	−0.476584	−	0.879129i	$-0.658125\pi$
$199$	−13.4461	−0.953168	−0.476584	+	0.879129i	$0.658125\pi$
$200$	19.2628	1.36209
$201$	−27.8769	−1.96628
$202$	−5.86808	−0.412876
$203$	−3.20889	−0.225220
$204$	5.23055	0.366212
$205$	−30.5177	−2.13145
$206$	3.52615	0.245678
$207$	−3.84076	−0.266951
$208$	0	0
$209$	21.9244	1.51654
$210$	6.48453	0.447475
$211$	11.9909	0.825490	0.412745	−	0.910847i	$-0.364570\pi$
$211$	11.9909	0.825490	0.412745	+	0.910847i	$0.364570\pi$
$212$	−10.7291	−0.736875
$213$	16.9482	1.16127
$214$	−9.44664	−0.645759
$215$	−30.2321	−2.06181
$216$	12.0502	0.819911
$217$	−4.83171	−0.327998
$218$	−1.45785	−0.0987384
$219$	−13.1727	−0.890130
$220$	−16.7569	−1.12975
$221$	0	0
$222$	18.3675	1.23274
$223$	−2.54948	−0.170726	−0.0853629	−	0.996350i	$-0.527205\pi$
$223$	−2.54948	−0.170726	−0.0853629	+	0.996350i	$0.527205\pi$
$224$	−5.24811	−0.350654
$225$	6.18575	0.412383
$226$	−10.3426	−0.687981
$227$	−8.99748	−0.597184	−0.298592	−	0.954381i	$-0.596517\pi$
$227$	−8.99748	−0.597184	−0.298592	+	0.954381i	$0.596517\pi$
$228$	10.2027	0.675691
$229$	7.21104	0.476519	0.238259	−	0.971202i	$-0.423423\pi$
$229$	7.21104	0.476519	0.238259	+	0.971202i	$0.423423\pi$
$230$	13.1965	0.870154
$231$	−9.12674	−0.600496
$232$	−9.48941	−0.623010
$233$	13.1933	0.864323	0.432162	−	0.901796i	$-0.357751\pi$
$233$	13.1933	0.864323	0.432162	+	0.901796i	$0.357751\pi$
$234$	0	0
$235$	−18.2439	−1.19010
$236$	−11.3067	−0.736007
$237$	15.8600	1.03022
$238$	−2.35349	−0.152554
$239$	15.9833	1.03387	0.516936	−	0.856024i	$-0.327073\pi$
$239$	15.9833	1.03387	0.516936	+	0.856024i	$0.327073\pi$
$240$	4.67292	0.301636
$241$	−25.1342	−1.61903	−0.809517	−	0.587096i	$-0.800271\pi$
$241$	−25.1342	−1.61903	−0.809517	+	0.587096i	$0.800271\pi$
$242$	−9.70235	−0.623691
$243$	9.53143	0.611442
$244$	−5.69643	−0.364677
$245$	3.39320	0.216784
$246$	−17.1874	−1.09583
$247$	0	0
$248$	−14.2884	−0.907316
$249$	14.5111	0.919602
$250$	−4.93939	−0.312394
$251$	−2.94037	−0.185594	−0.0927972	−	0.995685i	$-0.529581\pi$
$251$	−2.94037	−0.185594	−0.0927972	+	0.995685i	$0.529581\pi$
$252$	−1.02118	−0.0643286
$253$	−18.5737	−1.16772
$254$	10.5807	0.663894
$255$	−16.5048	−1.03357
$256$	−17.0101	−1.06313
$257$	18.5537	1.15735	0.578675	−	0.815559i	$-0.303570\pi$
$257$	18.5537	1.15735	0.578675	+	0.815559i	$0.303570\pi$
$258$	−17.0266	−1.06003
$259$	9.61127	0.597216
$260$	0	0
$261$	−3.04728	−0.188622
$262$	7.40066	0.457214
$263$	−10.3996	−0.641269	−0.320634	−	0.947203i	$-0.603896\pi$
$263$	−10.3996	−0.641269	−0.320634	+	0.947203i	$0.603896\pi$
$264$	−26.9898	−1.66111
$265$	33.8551	2.07970
$266$	−4.59071	−0.281475
$267$	−35.9728	−2.20150
$268$	−15.0839	−0.921394
$269$	2.74007	0.167065	0.0835324	−	0.996505i	$-0.473380\pi$
$269$	2.74007	0.167065	0.0835324	+	0.996505i	$0.473380\pi$
$270$	−13.2956	−0.809147
$271$	−11.0867	−0.673469	−0.336735	−	0.941600i	$-0.609323\pi$
$271$	−11.0867	−0.673469	−0.336735	+	0.941600i	$0.609323\pi$
$272$	−1.69599	−0.102834
$273$	0	0
$274$	−2.80396	−0.169394
$275$	29.9139	1.80387
$276$	−8.64343	−0.520273
$277$	9.14278	0.549336	0.274668	−	0.961539i	$-0.411432\pi$
$277$	9.14278	0.549336	0.274668	+	0.961539i	$0.411432\pi$
$278$	−7.10163	−0.425927
$279$	−4.58836	−0.274698
$280$	10.0344	0.599673
$281$	0.571443	0.0340895	0.0170447	−	0.999855i	$-0.494574\pi$
$281$	0.571443	0.0340895	0.0170447	+	0.999855i	$0.494574\pi$
$282$	−10.2749	−0.611860
$283$	18.7911	1.11701	0.558506	−	0.829500i	$-0.311375\pi$
$283$	18.7911	1.11701	0.558506	+	0.829500i	$0.311375\pi$
$284$	9.17047	0.544167
$285$	−32.1942	−1.90702
$286$	0	0
$287$	−8.99377	−0.530886
$288$	−4.98379	−0.293673
$289$	−11.0098	−0.647634
$290$	10.4702	0.614831
$291$	−13.7292	−0.804822
$292$	−7.12762	−0.417112
$293$	9.39283	0.548735	0.274368	−	0.961625i	$-0.411532\pi$
$293$	9.39283	0.548735	0.274368	+	0.961625i	$0.411532\pi$
$294$	1.91103	0.111454
$295$	35.6780	2.07725
$296$	28.4227	1.65203
$297$	18.7131	1.08585
$298$	5.40791	0.313272
$299$	0	0
$300$	13.9207	0.803713
$301$	−8.90960	−0.513541
$302$	8.53215	0.490970
$303$	−12.1279	−0.696727
$304$	−3.30819	−0.189738
$305$	17.9749	1.02924
$306$	−2.23495	−0.127764
$307$	−1.39399	−0.0795591	−0.0397796	−	0.999208i	$-0.512666\pi$
$307$	−1.39399	−0.0795591	−0.0397796	+	0.999208i	$0.512666\pi$
$308$	−4.93838	−0.281390
$309$	7.28767	0.414581
$310$	15.7652	0.895405
$311$	−10.0430	−0.569486	−0.284743	−	0.958604i	$-0.591908\pi$
$311$	−10.0430	−0.569486	−0.284743	+	0.958604i	$0.591908\pi$
$312$	0	0
$313$	29.0874	1.64411	0.822057	−	0.569405i	$-0.192826\pi$
$313$	29.0874	1.64411	0.822057	+	0.569405i	$0.192826\pi$
$314$	14.1675	0.799521
$315$	3.22230	0.181556
$316$	8.58169	0.482758
$317$	4.50428	0.252986	0.126493	−	0.991968i	$-0.459628\pi$
$317$	4.50428	0.252986	0.126493	+	0.991968i	$0.459628\pi$
$318$	19.0670	1.06923
$319$	−14.7364	−0.825082
$320$	21.8265	1.22014
$321$	−19.5239	−1.08972
$322$	3.88911	0.216732
$323$	11.6845	0.650145
$324$	11.7719	0.653994
$325$	0	0
$326$	−16.7766	−0.929168
$327$	−3.01302	−0.166621
$328$	−26.5966	−1.46855
$329$	−5.37660	−0.296422
$330$	29.7794	1.63930
$331$	14.2992	0.785953	0.392976	−	0.919549i	$-0.371445\pi$
$331$	14.2992	0.785953	0.392976	+	0.919549i	$0.371445\pi$
$332$	7.85179	0.430923
$333$	9.12721	0.500168
$334$	11.8477	0.648277
$335$	47.5965	2.60048
$336$	1.37714	0.0751293
$337$	28.4506	1.54981	0.774903	−	0.632081i	$-0.217799\pi$
$337$	28.4506	1.54981	0.774903	+	0.632081i	$0.217799\pi$
$338$	0	0
$339$	−21.3756	−1.16097
$340$	−8.93056	−0.484327
$341$	−22.1890	−1.20160
$342$	−4.35950	−0.235735
$343$	1.00000	0.0539949
$344$	−26.3477	−1.42057
$345$	27.2740	1.46838
$346$	−0.520097	−0.0279606
$347$	27.4960	1.47606	0.738032	−	0.674766i	$-0.235755\pi$
$347$	27.4960	1.47606	0.738032	+	0.674766i	$0.235755\pi$
$348$	−6.85774	−0.367614
$349$	−22.0281	−1.17914	−0.589570	−	0.807718i	$-0.700703\pi$
$349$	−22.0281	−1.17914	−0.589570	+	0.807718i	$0.700703\pi$
$350$	−6.26362	−0.334805
$351$	0	0
$352$	−24.1013	−1.28460
$353$	1.60451	0.0853993	0.0426996	−	0.999088i	$-0.486404\pi$
$353$	1.60451	0.0853993	0.0426996	+	0.999088i	$0.486404\pi$
$354$	20.0937	1.06797
$355$	−28.9370	−1.53582
$356$	−19.4645	−1.03162
$357$	−4.86407	−0.257434
$358$	−13.1225	−0.693545
$359$	21.4030	1.12961	0.564804	−	0.825225i	$-0.308952\pi$
$359$	21.4030	1.12961	0.564804	+	0.825225i	$0.308952\pi$
$360$	9.52907	0.502226
$361$	3.79185	0.199571
$362$	−1.76518	−0.0927761
$363$	−20.0524	−1.05248
$364$	0	0
$365$	22.4909	1.17723
$366$	10.1234	0.529156
$367$	−17.8326	−0.930856	−0.465428	−	0.885086i	$-0.654100\pi$
$367$	−17.8326	−0.930856	−0.465428	+	0.885086i	$0.654100\pi$
$368$	2.80260	0.146096
$369$	−8.54081	−0.444617
$370$	−31.3603	−1.63035
$371$	9.97733	0.517997
$372$	−10.3259	−0.535371
$373$	25.9981	1.34613	0.673066	−	0.739582i	$-0.264977\pi$
$373$	25.9981	1.34613	0.673066	+	0.739582i	$0.264977\pi$
$374$	−10.8081	−0.558873
$375$	−10.2085	−0.527164
$376$	−15.8998	−0.819969
$377$	0	0
$378$	−3.91832	−0.201537
$379$	−23.0715	−1.18510	−0.592552	−	0.805532i	$-0.701880\pi$
$379$	−23.0715	−1.18510	−0.592552	+	0.805532i	$0.701880\pi$
$380$	−17.4199	−0.893624
$381$	21.8677	1.12032
$382$	9.75919	0.499323
$383$	−7.91174	−0.404271	−0.202136	−	0.979358i	$-0.564788\pi$
$383$	−7.91174	−0.404271	−0.202136	+	0.979358i	$0.564788\pi$
$384$	−8.56727	−0.437197
$385$	15.5829	0.794176
$386$	4.48610	0.228336
$387$	−8.46087	−0.430090
$388$	−7.42874	−0.377137
$389$	−6.69526	−0.339463	−0.169732	−	0.985490i	$-0.554290\pi$
$389$	−6.69526	−0.339463	−0.169732	+	0.985490i	$0.554290\pi$
$390$	0	0
$391$	−9.89878	−0.500603
$392$	2.95722	0.149362
$393$	15.2953	0.771547
$394$	−8.75083	−0.440861
$395$	−27.0792	−1.36250
$396$	−4.68966	−0.235664
$397$	−38.8307	−1.94886	−0.974428	−	0.224698i	$-0.927860\pi$
$397$	−38.8307	−1.94886	−0.974428	+	0.224698i	$0.927860\pi$
$398$	12.9296	0.648104
$399$	−9.48786	−0.474987
$400$	−4.51374	−0.225687
$401$	−25.5291	−1.27486	−0.637431	−	0.770508i	$-0.720003\pi$
$401$	−25.5291	−1.27486	−0.637431	+	0.770508i	$0.720003\pi$
$402$	26.8061	1.33697
$403$	0	0
$404$	−6.56225	−0.326484
$405$	−37.1457	−1.84579
$406$	3.08564	0.153138
$407$	44.1386	2.18787
$408$	−14.3841	−0.712121
$409$	11.0908	0.548402	0.274201	−	0.961672i	$-0.411587\pi$
$409$	11.0908	0.548402	0.274201	+	0.961672i	$0.411587\pi$
$410$	29.3455	1.44927
$411$	−5.79510	−0.285851
$412$	3.94328	0.194272
$413$	10.5145	0.517387
$414$	3.69324	0.181513
$415$	−24.7760	−1.21620
$416$	0	0
$417$	−14.6773	−0.718751
$418$	−21.0823	−1.03117
$419$	−14.9846	−0.732044	−0.366022	−	0.930606i	$-0.619281\pi$
$419$	−14.9846	−0.732044	−0.366022	+	0.930606i	$0.619281\pi$
$420$	7.25163	0.353843
$421$	13.0941	0.638166	0.319083	−	0.947727i	$-0.396625\pi$
$421$	13.0941	0.638166	0.319083	+	0.947727i	$0.396625\pi$
$422$	−11.5304	−0.561289
$423$	−5.10581	−0.248253
$424$	29.5052	1.43290
$425$	15.9425	0.773326
$426$	−16.2972	−0.789602
$427$	5.29731	0.256355
$428$	−10.5642	−0.510638
$429$	0	0
$430$	29.0709	1.40192
$431$	25.1962	1.21366	0.606829	−	0.794832i	$-0.292441\pi$
$431$	25.1962	1.21366	0.606829	+	0.794832i	$0.292441\pi$
$432$	−2.82365	−0.135853
$433$	−20.0880	−0.965369	−0.482684	−	0.875794i	$-0.660338\pi$
$433$	−20.0880	−0.965369	−0.482684	+	0.875794i	$0.660338\pi$
$434$	4.64612	0.223021
$435$	21.6393	1.03753
$436$	−1.63031	−0.0780779
$437$	−19.3086	−0.923654
$438$	12.6668	0.605241
$439$	−29.7431	−1.41956	−0.709779	−	0.704424i	$-0.751205\pi$
$439$	−29.7431	−1.41956	−0.709779	+	0.704424i	$0.751205\pi$
$440$	46.0819	2.19687
$441$	0.949635	0.0452207
$442$	0	0
$443$	−4.81064	−0.228560	−0.114280	−	0.993449i	$-0.536456\pi$
$443$	−4.81064	−0.228560	−0.114280	+	0.993449i	$0.536456\pi$
$444$	20.5403	0.974800
$445$	61.4194	2.91156
$446$	2.45156	0.116085
$447$	11.1768	0.528645
$448$	6.43243	0.303904
$449$	19.5128	0.920866	0.460433	−	0.887695i	$-0.347694\pi$
$449$	19.5128	0.920866	0.460433	+	0.887695i	$0.347694\pi$
$450$	−5.94816	−0.280399
$451$	−41.3028	−1.94487
$452$	−11.5661	−0.544025
$453$	17.6338	0.828510
$454$	8.65189	0.406053
$455$	0	0
$456$	−28.0577	−1.31392
$457$	4.96981	0.232478	0.116239	−	0.993221i	$-0.462916\pi$
$457$	4.96981	0.232478	0.116239	+	0.993221i	$0.462916\pi$
$458$	−6.93407	−0.324008
$459$	9.97312	0.465505
$460$	14.7577	0.688079
$461$	−4.13305	−0.192495	−0.0962476	−	0.995357i	$-0.530684\pi$
$461$	−4.13305	−0.192495	−0.0962476	+	0.995357i	$0.530684\pi$
$462$	8.77619	0.408305
$463$	−24.3782	−1.13295	−0.566475	−	0.824079i	$-0.691693\pi$
$463$	−24.3782	−1.13295	−0.566475	+	0.824079i	$0.691693\pi$
$464$	2.22360	0.103228
$465$	32.5828	1.51099
$466$	−12.6866	−0.587694
$467$	16.1866	0.749028	0.374514	−	0.927221i	$-0.377810\pi$
$467$	16.1866	0.749028	0.374514	+	0.927221i	$0.377810\pi$
$468$	0	0
$469$	14.0270	0.647708
$470$	17.5431	0.809205
$471$	29.2808	1.34919
$472$	31.0938	1.43121
$473$	−40.9162	−1.88133
$474$	−15.2509	−0.700495
$475$	31.0975	1.42685
$476$	−2.63190	−0.120633
$477$	9.47483	0.433823
$478$	−15.3694	−0.702978
$479$	−3.89449	−0.177944	−0.0889719	−	0.996034i	$-0.528358\pi$
$479$	−3.89449	−0.177944	−0.0889719	+	0.996034i	$0.528358\pi$
$480$	35.3909	1.61536
$481$	0	0
$482$	24.1688	1.10086
$483$	8.03783	0.365734
$484$	−10.8501	−0.493187
$485$	23.4411	1.06440
$486$	−9.16533	−0.415748
$487$	18.1062	0.820470	0.410235	−	0.911980i	$-0.365447\pi$
$487$	18.1062	0.820470	0.410235	+	0.911980i	$0.365447\pi$
$488$	15.6653	0.709136
$489$	−34.6730	−1.56797
$490$	−3.26287	−0.147401
$491$	−15.5669	−0.702524	−0.351262	−	0.936277i	$-0.614247\pi$
$491$	−15.5669	−0.702524	−0.351262	+	0.936277i	$0.614247\pi$
$492$	−19.2206	−0.866533
$493$	−7.85374	−0.353715
$494$	0	0
$495$	14.7980	0.665122
$496$	3.34812	0.150335
$497$	−8.52794	−0.382530
$498$	−13.9537	−0.625281
$499$	−23.4892	−1.05152	−0.525761	−	0.850632i	$-0.676219\pi$
$499$	−23.4892	−1.05152	−0.525761	+	0.850632i	$0.676219\pi$
$500$	−5.52370	−0.247027
$501$	24.4862	1.09396
$502$	2.82743	0.126194
$503$	−15.2579	−0.680317	−0.340159	−	0.940368i	$-0.610481\pi$
$503$	−15.2579	−0.680317	−0.340159	+	0.940368i	$0.610481\pi$
$504$	2.80828	0.125091
$505$	20.7069	0.921445
$506$	17.8603	0.793985
$507$	0	0
$508$	11.8324	0.524978
$509$	−41.2509	−1.82842	−0.914208	−	0.405246i	$-0.867186\pi$
$509$	−41.2509	−1.82842	−0.914208	+	0.405246i	$0.867186\pi$
$510$	15.8708	0.702772
$511$	6.62822	0.293215
$512$	7.73507	0.341845
$513$	19.4536	0.858896
$514$	−17.8411	−0.786936
$515$	−12.4429	−0.548298
$516$	−19.0408	−0.838223
$517$	−24.6914	−1.08592
$518$	−9.24211	−0.406075
$519$	−1.07491	−0.0471834
$520$	0	0
$521$	−19.5558	−0.856756	−0.428378	−	0.903600i	$-0.640915\pi$
$521$	−19.5558	−0.856756	−0.428378	+	0.903600i	$0.640915\pi$
$522$	2.93023	0.128253
$523$	−16.4130	−0.717689	−0.358845	−	0.933397i	$-0.616829\pi$
$523$	−16.4130	−0.717689	−0.358845	+	0.933397i	$0.616829\pi$
$524$	8.27613	0.361545
$525$	−12.9454	−0.564982
$526$	10.0002	0.436029
$527$	−11.8256	−0.515130
$528$	6.32436	0.275232
$529$	−6.64237	−0.288799
$530$	−32.5547	−1.41409
$531$	9.98498	0.433311
$532$	−5.13378	−0.222578
$533$	0	0
$534$	34.5911	1.49690
$535$	33.3347	1.44119
$536$	41.4810	1.79171
$537$	−27.1209	−1.17035
$538$	−2.63482	−0.113595
$539$	4.59237	0.197808
$540$	−14.8685	−0.639838
$541$	33.7185	1.44967	0.724836	−	0.688922i	$-0.241916\pi$
$541$	33.7185	1.44967	0.724836	+	0.688922i	$0.241916\pi$
$542$	10.6609	0.457923
$543$	−3.64820	−0.156559
$544$	−12.8447	−0.550713
$545$	5.14439	0.220361
$546$	0	0
$547$	40.0637	1.71300	0.856501	−	0.516145i	$-0.172634\pi$
$547$	40.0637	1.71300	0.856501	+	0.516145i	$0.172634\pi$
$548$	−3.13566	−0.133949
$549$	5.03052	0.214697
$550$	−28.7649	−1.22654
$551$	−15.3195	−0.652633
$552$	23.7696	1.01170
$553$	−7.98042	−0.339362
$554$	−8.79161	−0.373520
$555$	−64.8140	−2.75120
$556$	−7.94173	−0.336804
$557$	−6.26450	−0.265435	−0.132718	−	0.991154i	$-0.542370\pi$
$557$	−6.26450	−0.265435	−0.132718	+	0.991154i	$0.542370\pi$
$558$	4.41212	0.186780
$559$	0	0
$560$	−2.35131	−0.0993611
$561$	−22.3376	−0.943096
$562$	−0.549494	−0.0231790
$563$	−18.9876	−0.800231	−0.400115	−	0.916465i	$-0.631030\pi$
$563$	−18.9876	−0.800231	−0.400115	+	0.916465i	$0.631030\pi$
$564$	−11.4904	−0.483831
$565$	36.4964	1.53542
$566$	−18.0693	−0.759510
$567$	−10.9471	−0.459735
$568$	−25.2190	−1.05817
$569$	40.9151	1.71525	0.857626	−	0.514274i	$-0.171939\pi$
$569$	40.9151	1.71525	0.857626	+	0.514274i	$0.171939\pi$
$570$	30.9577	1.29667
$571$	−18.9901	−0.794713	−0.397356	−	0.917664i	$-0.630072\pi$
$571$	−18.9901	−0.794713	−0.397356	+	0.917664i	$0.630072\pi$
$572$	0	0
$573$	20.1698	0.842606
$574$	8.64833	0.360974
$575$	−26.3448	−1.09866
$576$	6.10846	0.254519
$577$	6.42794	0.267599	0.133799	−	0.991008i	$-0.457282\pi$
$577$	6.42794	0.267599	0.133799	+	0.991008i	$0.457282\pi$
$578$	10.5869	0.440357
$579$	9.27166	0.385317
$580$	11.7088	0.486181
$581$	−7.30165	−0.302924
$582$	13.2019	0.547237
$583$	45.8196	1.89766
$584$	19.6011	0.811100
$585$	0	0
$586$	−9.03206	−0.373111
$587$	10.4081	0.429588	0.214794	−	0.976659i	$-0.431092\pi$
$587$	10.4081	0.429588	0.214794	+	0.976659i	$0.431092\pi$
$588$	2.13711	0.0881327
$589$	−23.0670	−0.950458
$590$	−34.3076	−1.41242
$591$	−18.0858	−0.743950
$592$	−6.66011	−0.273729
$593$	−16.2341	−0.666654	−0.333327	−	0.942811i	$-0.608171\pi$
$593$	−16.2341	−0.666654	−0.333327	+	0.942811i	$0.608171\pi$
$594$	−17.9944	−0.738319
$595$	8.30484	0.340465
$596$	6.04765	0.247721
$597$	26.7223	1.09367
$598$	0	0
$599$	4.84879	0.198116	0.0990580	−	0.995082i	$-0.468417\pi$
$599$	4.84879	0.198116	0.0990580	+	0.995082i	$0.468417\pi$
$600$	−38.2823	−1.56287
$601$	−35.9758	−1.46748	−0.733742	−	0.679428i	$-0.762228\pi$
$601$	−35.9758	−1.46748	−0.733742	+	0.679428i	$0.762228\pi$
$602$	8.56739	0.349181
$603$	13.3206	0.542455
$604$	9.54148	0.388237
$605$	34.2371	1.39193
$606$	11.6620	0.473738
$607$	28.7089	1.16526	0.582629	−	0.812738i	$-0.302024\pi$
$607$	28.7089	1.16526	0.582629	+	0.812738i	$0.302024\pi$
$608$	−25.0549	−1.01611
$609$	6.37725	0.258419
$610$	−17.2844	−0.699827
$611$	0	0
$612$	−2.49934	−0.101030
$613$	−37.1913	−1.50214	−0.751071	−	0.660221i	$-0.770462\pi$
$613$	−37.1913	−1.50214	−0.751071	+	0.660221i	$0.770462\pi$
$614$	1.34045	0.0540960
$615$	60.6499	2.44564
$616$	13.5807	0.547181
$617$	−0.556995	−0.0224238	−0.0112119	−	0.999937i	$-0.503569\pi$
$617$	−0.556995	−0.0224238	−0.0112119	+	0.999937i	$0.503569\pi$
$618$	−7.00776	−0.281893
$619$	−12.4079	−0.498715	−0.249358	−	0.968411i	$-0.580219\pi$
$619$	−12.4079	−0.498715	−0.249358	+	0.968411i	$0.580219\pi$
$620$	17.6302	0.708047
$621$	−16.4805	−0.661339
$622$	9.65725	0.387220
$623$	18.1007	0.725190
$624$	0	0
$625$	−15.1393	−0.605571
$626$	−27.9701	−1.11791
$627$	−43.5718	−1.74009
$628$	15.8435	0.632226
$629$	23.5235	0.937945
$630$	−3.09854	−0.123449
$631$	−10.5304	−0.419208	−0.209604	−	0.977786i	$-0.567217\pi$
$631$	−10.5304	−0.419208	−0.209604	+	0.977786i	$0.567217\pi$
$632$	−23.5999	−0.938752
$633$	−23.8304	−0.947174
$634$	−4.33127	−0.172017
$635$	−37.3366	−1.48166
$636$	21.3226	0.845496
$637$	0	0
$638$	14.1704	0.561012
$639$	−8.09844	−0.320369
$640$	14.6276	0.578207
$641$	17.8975	0.706910	0.353455	−	0.935452i	$-0.385007\pi$
$641$	17.8975	0.706910	0.353455	+	0.935452i	$0.385007\pi$
$642$	18.7740	0.740949
$643$	−11.7963	−0.465202	−0.232601	−	0.972572i	$-0.574724\pi$
$643$	−11.7963	−0.465202	−0.232601	+	0.972572i	$0.574724\pi$
$644$	4.34918	0.171382
$645$	60.0823	2.36574
$646$	−11.2357	−0.442064
$647$	4.52415	0.177863	0.0889313	−	0.996038i	$-0.471655\pi$
$647$	4.52415	0.177863	0.0889313	+	0.996038i	$0.471655\pi$
$648$	−32.3730	−1.27173
$649$	48.2867	1.89542
$650$	0	0
$651$	9.60239	0.376347
$652$	−18.7612	−0.734745
$653$	46.9198	1.83611	0.918057	−	0.396448i	$-0.129757\pi$
$653$	46.9198	1.83611	0.918057	+	0.396448i	$0.129757\pi$
$654$	2.89730	0.113293
$655$	−26.1150	−1.02040
$656$	6.23222	0.243327
$657$	6.29439	0.245568
$658$	5.17009	0.201551
$659$	−39.3468	−1.53273	−0.766366	−	0.642404i	$-0.777937\pi$
$659$	−39.3468	−1.53273	−0.766366	+	0.642404i	$0.777937\pi$
$660$	33.3022	1.29629
$661$	23.0664	0.897179	0.448590	−	0.893738i	$-0.351926\pi$
$661$	23.0664	0.897179	0.448590	+	0.893738i	$0.351926\pi$
$662$	−13.7499	−0.534406
$663$	0	0
$664$	−21.5926	−0.837955
$665$	16.1994	0.628187
$666$	−8.77663	−0.340088
$667$	12.9782	0.502519
$668$	13.2492	0.512628
$669$	5.06676	0.195892
$670$	−45.7684	−1.76819
$671$	24.3272	0.939143
$672$	10.4299	0.402343
$673$	−15.7225	−0.606057	−0.303028	−	0.952981i	$-0.597998\pi$
$673$	−15.7225	−0.606057	−0.303028	+	0.952981i	$0.597998\pi$
$674$	−27.3579	−1.05379
$675$	26.5427	1.02163
$676$	0	0
$677$	1.59613	0.0613443	0.0306721	−	0.999529i	$-0.490235\pi$
$677$	1.59613	0.0613443	0.0306721	+	0.999529i	$0.490235\pi$
$678$	20.5546	0.789395
$679$	6.90825	0.265114
$680$	24.5592	0.941804
$681$	17.8813	0.685213
$682$	21.3367	0.817026
$683$	18.4740	0.706889	0.353445	−	0.935455i	$-0.385010\pi$
$683$	18.4740	0.706889	0.353445	+	0.935455i	$0.385010\pi$
$684$	−4.87522	−0.186409
$685$	9.89445	0.378048
$686$	−0.961590	−0.0367137
$687$	−14.3310	−0.546762
$688$	6.17389	0.235377
$689$	0	0
$690$	−26.2264	−0.998422
$691$	26.1768	0.995813	0.497906	−	0.867231i	$-0.334102\pi$
$691$	26.1768	0.995813	0.497906	+	0.867231i	$0.334102\pi$
$692$	−0.581623	−0.0221100
$693$	4.36108	0.165664
$694$	−26.4399	−1.00365
$695$	25.0598	0.950572
$696$	18.8590	0.714847
$697$	−22.0122	−0.833772
$698$	21.1820	0.801752
$699$	−26.2200	−0.991731
$700$	−7.00459	−0.264749
$701$	−2.16383	−0.0817267	−0.0408634	−	0.999165i	$-0.513011\pi$
$701$	−2.16383	−0.0817267	−0.0408634	+	0.999165i	$0.513011\pi$
$702$	0	0
$703$	45.8850	1.73059
$704$	29.5401	1.11334
$705$	36.2573	1.36553
$706$	−1.54288	−0.0580670
$707$	6.10247	0.229507
$708$	22.4707	0.844500
$709$	34.7042	1.30334	0.651672	−	0.758501i	$-0.274068\pi$
$709$	34.7042	1.30334	0.651672	+	0.758501i	$0.274068\pi$
$710$	27.8256	1.04427
$711$	−7.57849	−0.284215
$712$	53.5279	2.00604
$713$	19.5416	0.731840
$714$	4.67725	0.175042
$715$	0	0
$716$	−14.6748	−0.548424
$717$	−31.7647	−1.18627
$718$	−20.5809	−0.768074
$719$	0.969723	0.0361646	0.0180823	−	0.999837i	$-0.494244\pi$
$719$	0.969723	0.0361646	0.0180823	+	0.999837i	$0.494244\pi$
$720$	−2.23289	−0.0832149
$721$	−3.66700	−0.136566
$722$	−3.64621	−0.135698
$723$	49.9509	1.85769
$724$	−1.97400	−0.0733632
$725$	−20.9021	−0.776286
$726$	19.2822	0.715628
$727$	−17.0417	−0.632040	−0.316020	−	0.948752i	$-0.602347\pi$
$727$	−17.0417	−0.632040	−0.316020	+	0.948752i	$0.602347\pi$
$728$	0	0
$729$	13.8988	0.514771
$730$	−21.6270	−0.800452
$731$	−21.8062	−0.806531
$732$	11.3209	0.418433
$733$	13.5638	0.500989	0.250494	−	0.968118i	$-0.419407\pi$
$733$	13.5638	0.500989	0.250494	+	0.968118i	$0.419407\pi$
$734$	17.1477	0.632933
$735$	−6.74354	−0.248739
$736$	21.2258	0.782392
$737$	64.4173	2.37284
$738$	8.21276	0.302316
$739$	−25.5091	−0.938366	−0.469183	−	0.883101i	$-0.655452\pi$
$739$	−25.5091	−0.938366	−0.469183	+	0.883101i	$0.655452\pi$
$740$	−35.0702	−1.28921
$741$	0	0
$742$	−9.59411	−0.352211
$743$	20.1185	0.738078	0.369039	−	0.929414i	$-0.379687\pi$
$743$	20.1185	0.738078	0.369039	+	0.929414i	$0.379687\pi$
$744$	28.3964	1.04106
$745$	−19.0831	−0.699150
$746$	−24.9996	−0.915299
$747$	−6.93391	−0.253698
$748$	−12.0867	−0.441932
$749$	9.82398	0.358960
$750$	9.81638	0.358444
$751$	−50.7696	−1.85261	−0.926305	−	0.376774i	$-0.877033\pi$
$751$	−50.7696	−1.85261	−0.926305	+	0.376774i	$0.877033\pi$
$752$	3.72570	0.135862
$753$	5.84360	0.212953
$754$	0	0
$755$	−30.1077	−1.09573
$756$	−4.38184	−0.159366
$757$	5.42838	0.197298	0.0986490	−	0.995122i	$-0.468548\pi$
$757$	5.42838	0.197298	0.0986490	+	0.995122i	$0.468548\pi$
$758$	22.1854	0.805808
$759$	36.9127	1.33985
$760$	47.9053	1.73771
$761$	−29.3194	−1.06283	−0.531414	−	0.847112i	$-0.678339\pi$
$761$	−29.3194	−1.06283	−0.531414	+	0.847112i	$0.678339\pi$
$762$	−21.0278	−0.761757
$763$	1.51609	0.0548860
$764$	10.9137	0.394843
$765$	7.88657	0.285139
$766$	7.60786	0.274883
$767$	0	0
$768$	33.8054	1.21985
$769$	−46.5006	−1.67686	−0.838428	−	0.545013i	$-0.816525\pi$
$769$	−46.5006	−1.67686	−0.838428	+	0.545013i	$0.816525\pi$
$770$	−14.9843	−0.539997
$771$	−36.8731	−1.32795
$772$	5.01679	0.180558
$773$	−15.5317	−0.558637	−0.279319	−	0.960198i	$-0.590109\pi$
$773$	−15.5317	−0.558637	−0.279319	+	0.960198i	$0.590109\pi$
$774$	8.13590	0.292439
$775$	−31.4729	−1.13054
$776$	20.4292	0.733366
$777$	−19.1011	−0.685250
$778$	6.43810	0.230817
$779$	−42.9370	−1.53838
$780$	0	0
$781$	−39.1635	−1.40138
$782$	9.51857	0.340384
$783$	−13.0757	−0.467287
$784$	−0.692948	−0.0247481
$785$	−49.9936	−1.78435
$786$	−14.7078	−0.524611
$787$	33.9561	1.21040	0.605202	−	0.796072i	$-0.293092\pi$
$787$	33.9561	1.21040	0.605202	+	0.796072i	$0.293092\pi$
$788$	−9.78603	−0.348613
$789$	20.6679	0.735797
$790$	26.0391	0.926428
$791$	10.7558	0.382430
$792$	12.8967	0.458264
$793$	0	0
$794$	37.3392	1.32512
$795$	−67.2826	−2.38627
$796$	14.4592	0.512492
$797$	5.90891	0.209304	0.104652	−	0.994509i	$-0.466627\pi$
$797$	5.90891	0.209304	0.104652	+	0.994509i	$0.466627\pi$
$798$	9.12344	0.322966
$799$	−13.1592	−0.465539
$800$	−34.1852	−1.20863
$801$	17.1891	0.607347
$802$	24.5485	0.866838
$803$	30.4393	1.07418
$804$	29.9772	1.05722
$805$	−13.7237	−0.483695
$806$	0	0
$807$	−5.44552	−0.191691
$808$	18.0464	0.634868
$809$	−30.4401	−1.07022	−0.535109	−	0.844783i	$-0.679730\pi$
$809$	−30.4401	−1.07022	−0.535109	+	0.844783i	$0.679730\pi$
$810$	35.7190	1.25504
$811$	−21.9976	−0.772442	−0.386221	−	0.922406i	$-0.626220\pi$
$811$	−21.9976	−0.772442	−0.386221	+	0.922406i	$0.626220\pi$
$812$	3.45066	0.121095
$813$	22.0334	0.772744
$814$	−42.4432	−1.48763
$815$	59.2001	2.07369
$816$	3.37055	0.117993
$817$	−42.5352	−1.48812
$818$	−10.6648	−0.372885
$819$	0	0
$820$	32.8170	1.14602
$821$	−0.557598	−0.0194603	−0.00973015	−	0.999953i	$-0.503097\pi$
$821$	−0.557598	−0.0194603	−0.00973015	+	0.999953i	$0.503097\pi$
$822$	5.57251	0.194364
$823$	9.50436	0.331301	0.165651	−	0.986185i	$-0.447028\pi$
$823$	9.50436	0.331301	0.165651	+	0.986185i	$0.447028\pi$
$824$	−10.8441	−0.377773
$825$	−59.4499	−2.06978
$826$	−10.1107	−0.351796
$827$	40.7855	1.41825	0.709125	−	0.705083i	$-0.249090\pi$
$827$	40.7855	1.41825	0.709125	+	0.705083i	$0.249090\pi$
$828$	4.13014	0.143532
$829$	2.74011	0.0951679	0.0475839	−	0.998867i	$-0.484848\pi$
$829$	2.74011	0.0951679	0.0475839	+	0.998867i	$0.484848\pi$
$830$	23.8243	0.826955
$831$	−18.1701	−0.630313
$832$	0	0
$833$	2.44749	0.0848006
$834$	14.1136	0.488712
$835$	−41.8074	−1.44680
$836$	−23.5762	−0.815401
$837$	−19.6884	−0.680530
$838$	14.4090	0.497751
$839$	4.66572	0.161078	0.0805392	−	0.996751i	$-0.474336\pi$
$839$	4.66572	0.161078	0.0805392	+	0.996751i	$0.474336\pi$
$840$	−19.9421	−0.688070
$841$	−18.7030	−0.644931
$842$	−12.5911	−0.433919
$843$	−1.13567	−0.0391145
$844$	−12.8944	−0.443843
$845$	0	0
$846$	4.90970	0.168799
$847$	10.0899	0.346693
$848$	−6.91377	−0.237420
$849$	−37.3448	−1.28167
$850$	−15.3302	−0.525821
$851$	−38.8724	−1.33253
$852$	−18.2251	−0.624382
$853$	−25.2886	−0.865864	−0.432932	−	0.901427i	$-0.642521\pi$
$853$	−25.2886	−0.865864	−0.432932	+	0.901427i	$0.642521\pi$
$854$	−5.09385	−0.174308
$855$	15.3835	0.526106
$856$	29.0517	0.992966
$857$	9.30340	0.317798	0.158899	−	0.987295i	$-0.449206\pi$
$857$	9.30340	0.317798	0.158899	+	0.987295i	$0.449206\pi$
$858$	0	0
$859$	42.4360	1.44790	0.723949	−	0.689854i	$-0.242325\pi$
$859$	42.4360	1.44790	0.723949	+	0.689854i	$0.242325\pi$
$860$	32.5099	1.10858
$861$	17.8739	0.609142
$862$	−24.2284	−0.825223
$863$	17.0172	0.579273	0.289636	−	0.957137i	$-0.406466\pi$
$863$	17.0172	0.579273	0.289636	+	0.957137i	$0.406466\pi$
$864$	−21.3852	−0.727538
$865$	1.83529	0.0624016
$866$	19.3165	0.656400
$867$	21.8805	0.743100
$868$	5.19575	0.176355
$869$	−36.6491	−1.24323
$870$	−20.8082	−0.705462
$871$	0	0
$872$	4.48340	0.151827
$873$	6.56032	0.222033
$874$	18.5669	0.628036
$875$	5.13668	0.173652
$876$	14.1652	0.478598
$877$	−39.3974	−1.33035	−0.665177	−	0.746685i	$-0.731644\pi$
$877$	−39.3974	−1.33035	−0.665177	+	0.746685i	$0.731644\pi$
$878$	28.6006	0.965225
$879$	−18.6670	−0.629623
$880$	−10.7981	−0.364004
$881$	9.92005	0.334215	0.167107	−	0.985939i	$-0.446557\pi$
$881$	9.92005	0.334215	0.167107	+	0.985939i	$0.446557\pi$
$882$	−0.913160	−0.0307477
$883$	−18.9158	−0.636568	−0.318284	−	0.947995i	$-0.603106\pi$
$883$	−18.9158	−0.636568	−0.318284	+	0.947995i	$0.603106\pi$
$884$	0	0
$885$	−70.9053	−2.38345
$886$	4.62586	0.155409
$887$	24.2260	0.813431	0.406715	−	0.913555i	$-0.366674\pi$
$887$	24.2260	0.813431	0.406715	+	0.913555i	$0.366674\pi$
$888$	−56.4863	−1.89556
$889$	−11.0034	−0.369041
$890$	−59.0603	−1.97971
$891$	−50.2732	−1.68421
$892$	2.74157	0.0917945
$893$	−25.6683	−0.858958
$894$	−10.7475	−0.359450
$895$	46.3058	1.54783
$896$	4.31086	0.144016
$897$	0	0
$898$	−18.7633	−0.626140
$899$	15.5044	0.517102
$900$	−6.65181	−0.221727
$901$	24.4195	0.813530
$902$	39.7164	1.32241
$903$	17.7067	0.589241
$904$	31.8071	1.05789
$905$	6.22888	0.207055
$906$	−16.9565	−0.563343
$907$	−20.0403	−0.665427	−0.332714	−	0.943028i	$-0.607964\pi$
$907$	−20.0403	−0.665427	−0.332714	+	0.943028i	$0.607964\pi$
$908$	9.67539	0.321089
$909$	5.79512	0.192212
$910$	0	0
$911$	32.5680	1.07903	0.539514	−	0.841977i	$-0.318608\pi$
$911$	32.5680	1.07903	0.539514	+	0.841977i	$0.318608\pi$
$912$	6.57459	0.217707
$913$	−33.5319	−1.10974
$914$	−4.77892	−0.158073
$915$	−35.7227	−1.18095
$916$	−7.75435	−0.256211
$917$	−7.69627	−0.254153
$918$	−9.59006	−0.316519
$919$	−43.7858	−1.44436	−0.722181	−	0.691705i	$-0.756860\pi$
$919$	−43.7858	−1.44436	−0.722181	+	0.691705i	$0.756860\pi$
$920$	−40.5839	−1.33801
$921$	2.77037	0.0912868
$922$	3.97430	0.130887
$923$	0	0
$924$	9.81439	0.322870
$925$	62.6061	2.05848
$926$	23.4418	0.770346
$927$	−3.48231	−0.114374
$928$	16.8406	0.552821
$929$	−47.7826	−1.56770	−0.783848	−	0.620953i	$-0.786746\pi$
$929$	−47.7826	−1.56770	−0.783848	+	0.620953i	$0.786746\pi$
$930$	−31.3313	−1.02740
$931$	4.77408	0.156464
$932$	−14.1874	−0.464722
$933$	19.9591	0.653433
$934$	−15.5649	−0.509299
$935$	38.1389	1.24728
$936$	0	0
$937$	−18.7762	−0.613393	−0.306696	−	0.951807i	$-0.599224\pi$
$937$	−18.7762	−0.613393	−0.306696	+	0.951807i	$0.599224\pi$
$938$	−13.4883	−0.440407
$939$	−57.8073	−1.88647
$940$	19.6184	0.639883
$941$	−41.5379	−1.35410	−0.677049	−	0.735938i	$-0.736741\pi$
$941$	−41.5379	−1.35410	−0.677049	+	0.735938i	$0.736741\pi$
$942$	−28.1561	−0.917377
$943$	36.3749	1.18453
$944$	−7.28603	−0.237140
$945$	13.8267	0.449783
$946$	39.3447	1.27921
$947$	−33.6878	−1.09471	−0.547353	−	0.836902i	$-0.684364\pi$
$947$	−33.6878	−1.09471	−0.547353	+	0.836902i	$0.684364\pi$
$948$	−17.0550	−0.553920
$949$	0	0
$950$	−29.9030	−0.970183
$951$	−8.95167	−0.290278
$952$	7.23778	0.234578
$953$	−30.0769	−0.974286	−0.487143	−	0.873322i	$-0.661961\pi$
$953$	−30.0769	−0.974286	−0.487143	+	0.873322i	$0.661961\pi$
$954$	−9.11090	−0.294976
$955$	−34.4376	−1.11438
$956$	−17.1875	−0.555884
$957$	29.2867	0.946706
$958$	3.74490	0.120992
$959$	2.91596	0.0941614
$960$	−43.3774	−1.40000
$961$	−7.65460	−0.246922
$962$	0	0
$963$	9.32919	0.300629
$964$	27.0279	0.870510
$965$	−15.8303	−0.509595
$966$	−7.72910	−0.248680
$967$	−0.586833	−0.0188713	−0.00943564	−	0.999955i	$-0.503004\pi$
$967$	−0.586833	−0.0188713	−0.00943564	+	0.999955i	$0.503004\pi$
$968$	29.8381	0.959032
$969$	−23.2215	−0.745981
$970$	−22.5407	−0.723739
$971$	6.42217	0.206097	0.103049	−	0.994676i	$-0.467140\pi$
$971$	6.42217	0.206097	0.103049	+	0.994676i	$0.467140\pi$
$972$	−10.2496	−0.328755
$973$	7.38529	0.236762
$974$	−17.4107	−0.557876
$975$	0	0
$976$	−3.67076	−0.117498
$977$	−29.2836	−0.936867	−0.468433	−	0.883499i	$-0.655181\pi$
$977$	−29.2836	−0.936867	−0.468433	+	0.883499i	$0.655181\pi$
$978$	33.3412	1.06614
$979$	83.1253	2.65670
$980$	−3.64886	−0.116559
$981$	1.43973	0.0459670
$982$	14.9690	0.477679
$983$	−39.4156	−1.25716	−0.628581	−	0.777745i	$-0.716364\pi$
$983$	−39.4156	−1.25716	−0.628581	+	0.777745i	$0.716364\pi$
$984$	52.8572	1.68503
$985$	30.8794	0.983899
$986$	7.55209	0.240507
$987$	10.6853	0.340116
$988$	0	0
$989$	36.0345	1.14583
$990$	−14.2296	−0.452248
$991$	24.3027	0.772000	0.386000	−	0.922499i	$-0.373856\pi$
$991$	24.3027	0.772000	0.386000	+	0.922499i	$0.373856\pi$
$992$	25.3573	0.805096
$993$	−28.4177	−0.901809
$994$	8.20039	0.260100
$995$	−45.6253	−1.44642
$996$	−15.6044	−0.494444
$997$	−46.4460	−1.47096	−0.735479	−	0.677547i	$-0.763043\pi$
$997$	−46.4460	−1.47096	−0.735479	+	0.677547i	$0.763043\pi$
$998$	22.5870	0.714980
$999$	39.1643	1.23910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.r.1.5	yes	12
7.6	odd	2		8281.2.a.cq.1.5		12
13.5	odd	4		1183.2.c.j.337.15		24
13.8	odd	4		1183.2.c.j.337.10		24
13.12	even	2		1183.2.a.q.1.8	✓	12
91.90	odd	2		8281.2.a.cn.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.8	✓	12	13.12	even	2
1183.2.a.r.1.5	yes	12	1.1	even	1	trivial
1183.2.c.j.337.10		24	13.8	odd	4
1183.2.c.j.337.15		24	13.5	odd	4
8281.2.a.cn.1.8		12	91.90	odd	2
8281.2.a.cq.1.5		12	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q-0.961590 q^{2} -1.98737 q^{3} -1.07534 q^{4} +3.39320 q^{5} +1.91103 q^{6} +1.00000 q^{7} +2.95722 q^{8} +0.949635 q^{9} +O(q^{10})\)	\(q-0.961590 q^{2} -1.98737 q^{3} -1.07534 q^{4} +3.39320 q^{5} +1.91103 q^{6} +1.00000 q^{7} +2.95722 q^{8} +0.949635 q^{9} -3.26287 q^{10} +4.59237 q^{11} +2.13711 q^{12} -0.961590 q^{14} -6.74354 q^{15} -0.692948 q^{16} +2.44749 q^{17} -0.913160 q^{18} +4.77408 q^{19} -3.64886 q^{20} -1.98737 q^{21} -4.41598 q^{22} -4.04446 q^{23} -5.87709 q^{24} +6.51382 q^{25} +4.07483 q^{27} -1.07534 q^{28} -3.20889 q^{29} +6.48453 q^{30} -4.83171 q^{31} -5.24811 q^{32} -9.12674 q^{33} -2.35349 q^{34} +3.39320 q^{35} -1.02118 q^{36} +9.61127 q^{37} -4.59071 q^{38} +10.0344 q^{40} -8.99377 q^{41} +1.91103 q^{42} -8.90960 q^{43} -4.93838 q^{44} +3.22230 q^{45} +3.88911 q^{46} -5.37660 q^{47} +1.37714 q^{48} +1.00000 q^{49} -6.26362 q^{50} -4.86407 q^{51} +9.97733 q^{53} -3.91832 q^{54} +15.5829 q^{55} +2.95722 q^{56} -9.48786 q^{57} +3.08564 q^{58} +10.5145 q^{59} +7.25163 q^{60} +5.29731 q^{61} +4.64612 q^{62} +0.949635 q^{63} +6.43243 q^{64} +8.77619 q^{66} +14.0270 q^{67} -2.63190 q^{68} +8.03783 q^{69} -3.26287 q^{70} -8.52794 q^{71} +2.80828 q^{72} +6.62822 q^{73} -9.24211 q^{74} -12.9454 q^{75} -5.13378 q^{76} +4.59237 q^{77} -7.98042 q^{79} -2.35131 q^{80} -10.9471 q^{81} +8.64833 q^{82} -7.30165 q^{83} +2.13711 q^{84} +8.30484 q^{85} +8.56739 q^{86} +6.37725 q^{87} +13.5807 q^{88} +18.1007 q^{89} -3.09854 q^{90} +4.34918 q^{92} +9.60239 q^{93} +5.17009 q^{94} +16.1994 q^{95} +10.4299 q^{96} +6.90825 q^{97} -0.961590 q^{98} +4.36108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

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